-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
1/24
1 1 D i v i s i b i l i t y R u l e s a n d P r i m e F a c t o r i z a t i o nC h a p t e r s 5 . 1 - 2 , D a t e _ _ _ _ _
2 i f t h e n u m b e r i s e v e n
3 i f t h e s u m o f i t s d i g i t s i s d i v i s i b l e b y 3
5 i f t h e l a s t d i g i t i s 0 o r 5
1 0 i f t h e l a s t d i g i t i s 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
2/24
5 4 0 7 5 2 2 3 3 1 4 5 , 2 1 5
2
3
5
1 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
3/24
5 4 0 7 5 2 2 3 3 1 4 5 , 2 1 5
2
3
5
1 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
4/24
4 8 0 4 5 9 6 7 5 5 6 , 3 6 0
2
3
5
1 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
5/24
4 8 0 4 5 9 6 7 5 5 6 , 3 6 0
2
3
5
1 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
6/24
F i n d i n g F a c t o r s
A n a t u r a l n u m b e r i s f a c t o r e d w h e n i t i s w r i t t e n
a s t h e p r o d u c t o f t w o o r m o r e n a t u r a l n u m b e r s .
N a t u r a l n u m b e r s a r e t h e c o u n t i n g n u m b e r s : 1 ,
2 , 3 , 4 , e t c .
F o r i n s t a n c e , 3 2 c a n b e f a c t o r e d a s 4 8 . T h en u m b e r s 4 a n d 8 a r e f a c t o r s o f 3 2 .
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
7/24
H o w d o w e l i s t a l l o f t h e f a c t o r s f o r 2 4 ?
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
8/24
H o w d o w e l i s t a l l o f t h e f a c t o r s f o r 2 4 ?
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
9/24
L i s t a l l o f t h e f a c t o r s f o r 3 6 .
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
10/24
L i s t a l l o f t h e f a c t o r s f o r 3 6 .
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
11/24
L i s t a l l o f t h e f a c t o r s f o r e a c h n u m b e rf r o m l e a s t t o g r e a t e s t .
A . 1 5
B . 4 0
C . 4 5
D . 6 4
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
12/24
L i s t a l l o f t h e f a c t o r s f o r e a c h n u m b e rf r o m l e a s t t o g r e a t e s t .
A . 1 5
B . 4 0
C . 4 5
D . 6 4
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
13/24
A n a t u r a l n u m b e r i s p r i m e i f i t h a s e x a c t l y t w o
f a c t o r s , i t s e l f a n d 1 .
E x a m p l e s : 2 , 3 , 5 , 7 , 1 1 , 1 3 , . . .
A n a t u r a l n u m b e r i s c o m p o s i t e i f i t h a s t h r e e o r
m o r e f a c t o r s .
E x a m p l e s : 4 , 6 , 8 , 9 , 1 0 , 1 2 , . . .
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
14/24
I s t h e n u m b e r p r i m e o r c o m p o s i t e ?
1 3 p r i m e
2 6 c o m p o s i t e
2 9 p r i m e
1 n e i t h e r
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
15/24
F a c t o r T r e e s
U s e f a c t o r t r e e s t o f a c t o r a n u m b e r u n t i la l l o f i t s f a c t o r s a r e p r i m e .
2 8
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
16/24
W r i t e t h e p r i m e f a c t o r i z a t i o n o f 4 0 .
4 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
17/24
W r i t e t h e p r i m e f a c t o r i z a t i o n o f 4 0 .
4 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
18/24
W r i t e t h e p r i m e f a c t o r i z a t i o n o f e a c h n u m b e r .
1 6 1 2 5
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
19/24
W r i t e t h e p r i m e f a c t o r i z a t i o n o f e a c h n u m b e r .
1 6 1 2 5
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
20/24
U s e a f a c t o r t r e e t o w r i t e t h e p r i m e
f a c t o r i z a t i o n o f e a c h n u m b e r .
E . 4 2 F . 6 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
21/24
U s e a f a c t o r t r e e t o w r i t e t h e p r i m e
f a c t o r i z a t i o n o f e a c h n u m b e r .
E . 4 2 F . 6 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
22/24
U s e a f a c t o r t r e e t o w r i t e t h e p r i m e
f a c t o r i z a t i o n o f e a c h n u m b e r .
G . 3 6 H . 7 5
I . 2 1 J . 2 0 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
23/24
U s e a f a c t o r t r e e t o w r i t e t h e p r i m e
f a c t o r i z a t i o n o f e a c h n u m b e r .
G . 3 6 H . 7 5
I . 2 1 J . 2 0 0
-
8/17/2019 11 Divisibility Rules and Prime Factorization Notes
24/24